Continuity mistake: The crew on the destroyer imposing the blockade initially saw the two Russian freighters on their radar screen, and then they saw a third 'blip' on the radar screen as the ships approached the blockade. The radarman identified the first two blips as surface ships, and the third blip as a submarine. Unless that was a sonar display, they would never have seen the submarine. The third contact would have been made by the ship's sonarman, and the two surface contacts would have been identified by the radarman.
Continuity mistake: The Pierce fires its guns to clear the barrels of the already loaded starshell. This is technically correct but when the starshells burst there are four of them i.e. the same as the number of gun barrels on the Pierce. Earlier however, when the Pierce first confronts the Grozny, there is a shot in the 5in gun turret showing at least one barrel being loaded with practice shell (i.e. solid shot). The Captain reports to the Admiral that the guns are loaded. (01:30:15)
Continuity mistake: When the U2 gets shot down, the missiles launched appear to be truck launched SA3s. The only missiles that the Soviets possessed at the time that could get anywhere near the altitude of a U2 are SA2s, which are taller than telephone poles.
Continuity mistake: In the final interception of a Russian ship, the vessel is described as a tanker, but in reality, the ship shown on the screen is a freighter.
Continuity mistake: In a scene where O'Donnell meets with Kennedy in his private quarters, Kennedy unties his tie and leaves it hanging around his shoulders. A moment later it has somehow crawled partially back up under his collar.
Continuity mistake: There were several flash frames in the film - the most obvious was when an eight appeared in an atomic bomb shot. The eight was from film leader and the result of a bad edit.
Continuity mistake: When the President and advisors are sitting around a large table and communicating with the captain of the ship at the beginning of the blockade, when viewed from the front, the President clearly has his right hand up to his chin while concerned and deep in thought. As the camera angle switches to his back several times, his left hand is on his chin. Front angle right, rear angle left.
Continuity mistake: When they show the Cubans building the missile base they show an "army" military truck, a mid 80s Kenworth, not an early 60s.
Continuity mistake: When the US warship fires its guns at the freighter, you can see how the crew loads the guns. They load up blue grenades with white letters - blue rounds are training rounds.
Continuity mistake: When O'Donnell drives Robert Kennedy to meet with the Russian Ambassador to avert WW III, the exterior of the car changes from rain-soaked to bone dry several times during the drive.